Extraction of Moment Closures for Strongly Non-Equilibrium Flows via Machine Learning

TL;DR

This paper presents a machine learning approach to derive moment closures for modeling strongly non-equilibrium gas flows, enabling accurate predictions of shock structures and hypersonic scenarios beyond traditional CFD capabilities.

Contribution

It introduces a data-driven closure modeling framework using high-order moments trained on DSMC data, bridging machine learning with continuum mechanics for rarefied gas flows.

Findings

Accurately predicts normal shock structures.

Generalizes to hypersonic and unsteady flows.

Preserves physical structure through thermodynamic consistency.

Abstract

We introduce a machine learning framework for moment-equation modeling of rarefied gas flows, addressing strongly non-equilibrium conditions inaccessible to conventional computational fluid dynamics. Our approach utilizes high-order moments and collision integrals, highly sensitive to non-equilibrium effects, as key predictive variables. Training datasets are created from one-dimensional steady shock simulations, and a methodology of computing collision integrals is developed. By learning thermodynamically consistent closures directly from DSMC data, our R13-ML model, combined with a discontinuous Galerkin solver for the transfer equations of moments, preserves physical structure and accurately predicts normal shock structures and generalizes to hypersonic and some unsteady, one-dimensional wave scenarios. This work bridges machine learning with continuum mechanics, offering a road map for high-fidelity aerothermal predictions in next-generation supersonic vehicles.